I am trying to understand the intuition behind why a convexity adjustment is required when calculating the YoY rate on inflation swaps.
(Assume no lags for simplicity). The current inflation index is 100. The 3y zero coupon inflation rate in the market is 3% The 4y zero coupon inflation rate in the market is 4%.
This means, the projected inflation index in Year 3 = 100 x (1+3%)^3 = 109.2727 The projected inflation index in year 4 = 100 x (1+4%)^4 = 116.985856
Therefore the YoY rate between years 3 and 4 = 116.985856 / 109.2727 - 1 = 7.0586%.
However, literature tells you that you need to add a convexity adjustment to this and I'm trying to understand why. Both the 3y and 4y are based on market projections, so shouldn't it follow the YoY is also based on that?
